Introduces the C-constrained Gromov-Hausdorff distance for chromatic metric pairs and proves that all six diagrams in a six-pack are stable in bottleneck distance with respect to it, up to a factor of 2.
A Distance Between Filtered Spaces Via Tripods
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We present a simplified treatment of stability of filtrations on finite spaces. Interestingly, we can lift the stability result for combinatorial filtrations from [CSEM06] to the case when two filtrations live on different spaces without directly invoking the concept of interleaving. We then prove that this distance is intrinsic by constructing explicit geodesics between any pair of filtered spaces. Finally we use this construction to obtain a strengthening of the stability result.
citation-role summary
method 1
citation-polarity summary
fields
math.MG 1years
2025 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
Introduces the C-constrained Gromov-Hausdorff distance for chromatic metric pairs and proves that all six diagrams in a six-pack are stable in bottleneck distance with respect to it, up to a factor of 2.